f(x) = 1/(2x-1) let f(x) = y so I have less to type
y = 1/(2x - 1) solve for x:
(2x - 1)y = 1 get rid of the denominator multiply both sides by (2x - 1).
2x-1 = 1/y divide both sides by y
2x = 1/y + 1 add 1 to both sides
x = 1/2(y + 1) divide both sides by 2
x = 1/2y + 2 distribute the 2
change x for y to get the inverse
y = 1/2x + 2 is the inverse